ALGORITHMIC PROBLEMS FOR FINITE-GROUPS AND FINITE 0-SIMPLE SEMIGROUPS

It is shown that the embeddability of a finite 4-nilpotent semigroup i nto a 0-simple finite semigroup with maximal groups from a pseudovarie ty V is decidable if and only if the universal theory of the class V i s decidable. We show that it is impossible to replace 4 by 3 in this s tatement. We also show that if the membership in V is decidable then t he membership in the pseudovariety generated by the class of all finit e 0-simple semigroups with subgroups from V is decidable while the mem bership in the quasi-variety generated by this class of 0-simple semig roups may be undecidable. (C) 1997 Published by Elsevier Science B.V.